Search: id:A005991 Results 1-1 of 1 results found. %I A005991 M1582 %S A005991 2,6,12,20,30,43 %N A005991 Let k(n) denote the least integer such that every n X n (0,1)-matrix with exactly k(n) ones in each row and in each column contains a 2 X 2 submatrix without zeros. The sequence gives the index n of the last term in each string of equal entries in k(n). %C A005991 1 is not in the sequence because a 1 X 1 matrix does not contain a 2 X 2 submatrix. - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008 %D A005991 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %D A005991 Problem E2429, Amer. Math. Monthly, 81 (1974), 1112-1113. %H A005991 Index entries for sequences related to binary matrices %e A005991 Since k(2) = 2 then a(1) = 2 %e A005991 Since k(3) = k(4) = k(5) = k(6) = 3 then a(2) = 6 %e A005991 Since k(7) = k(8) = ... = k(12) = 4 then a(3) = 12 %e A005991 Since k(13) = k(14) = ... = k(20) = 5 then a(4) = 20 %e A005991 Since k(21) = k(22) = ... = k(30) = 6 then a(5) = 30 %e A005991 Since k(31) = k(32) = ... = k(43) = 7 then a(6) = 43 %Y A005991 Sequence in context: A160929 A103505 A002378 this_sequence A003274 A121315 A078878 %Y A005991 Adjacent sequences: A005988 A005989 A005990 this_sequence A005992 A005993 A005994 %K A005991 nonn,more %O A005991 1,1 %A A005991 N. J. A. Sloane (njas(AT)research.att.com). %E A005991 Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008 Search completed in 0.001 seconds